How auto- and cross-correlations in link dynamics influence diffusion in non-Markovian temporal networks
Many real-world biological, social and man-made networks are inherently dynamic, with their links switching on and off over time. In particular, the evolution of these networks is often observed to be non-Markovian, and the dynamics of their links are often correlated. Hence, to accurately model these networks, the inclusion of both memory and dynamical dependencies between links is key. This being said, the interplay between memory and correlations in the dynamics of links, and its effects on processes taking place on the network, is not well understood. In light of this, we here introduce a simple generative model for temporal networks with a specified underlying structural backbone, and with precise control over the dynamical dependencies between links and the strength and length of their memories. In our model the presence of each link is influenced not only by its past activity, but also by the past activities of other links, as specified by a coupling matrix, which directly controls the interactions, and hence the correlations, among links. The model allows us to study the effects of both the memory parameter and correlations between links on the speed of a diffusion process over the network, as measured by the time taken for it to reach equilibrium. Further to this, we can effectively separate the roles of autocorrelations and neighbourhood correlations in link dynamics, allowing us to show, through both numerical simulations and analytical results, that not only is the speed of diffusion non-monotonically dependent on the memory length, but also that correlations among neighbouring links help to speed up the spreading process, while autocorrelations slow it back down. Our results have implications in the study of opinion formation, the modelling of social networks and the spreading of epidemics through mobile populations.